Response of corrugated interface on incident qSV-wave in monoclinic elastic half-spaces

• Autorzy: Singh S. S. , Lalvohbika J.

Identyfikatory

DOI

10.2478/ijame-2018-0040

• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with the problem of reflection and transmission of elastic waves due to an incident plane qSV-wave at a corrugated interface between two dissimilar monoclinic elastic half-spaces. Due to the corrugated nature of the interface, there exist regularly and irregularly reflected and transmitted elastic waves. Using Rayleigh’s method of approximation, the reflection and transmission coefficients of regular and irregular waves are obtained for the first order of approximation. We have found that these coefficients are functions of the angle of incidence, elastic constants, corrugation and the frequency parameter. These coefficients are obtained for a special type of interface, z =dcos py. We have computed these coefficients for a particular model and discussed the effects of corrugation and frequency parameter.

Słowa kluczowe

EN

qSV and qP-waves; reflection and transmission coefficients; monoclinic medium; corrugated interface; phase velocity

PL

współczynnik odbicia; współczynnik transmisji; prędkość fazowa

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2018
• Tom: Vol. 23, no. 3
• Strony: 727--750
• Opis fizyczny: Bibliogr. 30 poz., rys., wykr.

Twórcy

autor

Singh S. S.

• Department of Mathematics and Computer Science Mizoram University, Aizawl -796 004 Mizoram, INDIA

autor

Lalvohbika J.

• Department of Mathematics, Pachhunga University College Aizawl -796 001, Mizoram, INDIA

Bibliografia

• [1] Chattopadhyay A. and Choudhury S. (1995): The reflection phenomena of P-waves in a medium of monoclinic type. – Int. J. Engng. Sci., vol.33, No.2, pp.195-207.
• [2] Chattopadhyay A., Saha S. and Chakraborty M. (1997): Reflection and transmission of shear waves in monoclinic media. – Int. J. Num. Analy. Methods Geomech., vol.21, No.7, pp.495-504.
• [3] Dowaik M.A. and Ogden R.W. (1991): Interfacial waves and deformations in pre-stressed elastic media. – Proc. Royal Soc. Lon. A, vol.433, pp.313-328.
• [4] Sheriff R.E. and Geldart P.L. (1995): Exploration Seismology. – Cambridge: Cambridge University Press.
• [5] Singh S.J. (1999): Comments on “The reflection phenomena of P-waves in a medium of monoclinic type by Chattopadhyay A and Choudhury”. – Int. J. Engng. Sci., vol.37, No.3, pp. 407-410.
• [6] Singh S.J. and Khurana S. (2002): Reflection of P and SV-waves at the free surface of a monoclinic elastic halfspace. – Proc. Indian Acad. Sci.(Earth Planet Science), vol.111, No.4, pp.401-412.
• [7] Udias A.(1999): Principles of Seismology. – Cambridge: Cambridge University Press.
• [8] Chattopadhyay A. and Saha S. (1996): Reflection and refraction of P-waves at the interface of two monoclinic media. – Int. J. Engng. Sci., vol.34, No.11, pp.1271-1284.
• [9] Chattopadhyay A. and Saha S. (1999): Reflection and refraction of quasi-SV waves at the interface of the monoclinic media. – Acta Geophys. Pol., vol.47, No.3, pp.307-322. ADDENDUM in Acta Geophys. Pol. (2003), vol.51, No.4, pp.473-475.
• [10] Nayfeh A.H. (1991): Elastic wave reflection from liquid-anisotropic substrate interfaces. – Wave Motion, vol.14, No.1, pp.55-67.
• [11] Singh S.J. and Khurana S. (2001): Reflection and transmission of P- and SV-waves at the interface between two monoclinic elastic half-spaces. – Proc. Nat. Acad. Sci. A, vol.71, No.4, pp. 305-319.
• [12] Rayleigh L. (1907): On the dynamical theory of gratings. – Proc. Royal Soc. Lond. A, vol.79, pp.399-416.
• [13] Abubakar I. (1962): Scattering of plane elastic waves at rough surfaces I. – Proc. Camb. Phil. Soc., vol.58, pp.136- 157.
• [14] Asano S. (1966): Reflection and refraction of elastic waves at a corrugated interface. – Bull. Seism. Soc. Am., vol.56, No.1, pp.201-221.
• [15] Dunkin J.W. and Eringen A.C. (1962): Reflection of elastic waves from the wavy boundary of a half space. – Int. Proc. 4th US National Cong. Appl. Mech., ASME Publication, pp.143-160.
• [16] Gupta S.K. (1978): Reflections and refractions from curved interfaces: model study. – Geophys. Prosp., vol.26, No.1, pp.82-96.
• [17] Kuo J.T. and Nafe J.E. (1962): Period equation for Rayleigh waves in a layer overlaying a half space with a sinusoidal interface. – Bull. Seism. Soc. Am., vol. 52, No.4, pp.807-822.
• [18] Levy A. and Deresiewicz H. (1967): Reflections and transmission of elastic waves in a system of corrugated layers. – Bull. Seism. Soc. Am., vol.57, No.3, pp.393-419.
• [19] Rice O. (1951): Reflection of electromagnetic waves from slightly rough surfaces. – Comm. Pure Appl. Maths., vol.4, No.2-3, pp.351-378.
• [20] Singh S.S. and Tomar S.K. (2007): Elastic waves at a corrugated interface between two dissimilar fibre-reinforced elastic half-spaces. – Int. J. Num. Analy. Methods Geomech., vol.31, No.9, pp.1085-1116.
• [21] Singh S.S. and Tomar S.K. (2008): qP-wave at a corrugated interface between two dissimilar pre-stressed elastic half-spaces. – J. Sound Vibra., vol.317, No.(3-5), pp.687-708.
• [22] Tomar S.K. and Kaur J. (2003): Reflection and transmission of SH-waves at a corrugated interface between two laterally and vertically heterogeneous anisotropic elastic solid half-spaces. – Earth, Planets Space, vol.55, No.9, pp.531-547.
• [23] Chattopadhyay A., Gupta S., Sharma V.K. and Kumari P. (2009): Reflection and refraction of plane quasi-P waves at a corrugated interface between distinct triclinic elastic half spaces. – Int. J. Solids Struct., vol.46, No.17, pp.3241-3256.
• [24] Kaur J. and Tomar S.K. (2004): Reflection and refraction of SH-waves at a corrugated interface between two monoclinic elastic half-spaces. – Int. J. Num. Analy. Methods Geomech., vol.28, No.15, pp.1543-1575.
• [25] Kennett B.L.N. (1972): Seismic wave scattering by obstacles on interfaces. – Geophys. J. Int., vol.28, No.3, pp.249-266.
• [26] Paul A. and Campillo M. (1988): Diffraction and conversion of elastic waves at a corrugated interface. – Geophys., vol.53, No.11, pp.1415-1424.
• [27] Yu C.W. and Dravinski M. (2009): Scattering of plane harmonic P, SV or Rayleigh waves by a completely embedded corrugated cavity. – Geophys. J. Int., vol.178, No.1, pp.479-487.
• [28] Singh S.S. and Singh J. (2013): Effect of corrugation on incident qSV-waves in pre-stressed elastic half-space. – Int. J. Appl. Maths. Mech., vol.9, No.9, pp.92-106.
• [29] Singh S.S. and Tomar S.K. (2007): Quasi P-waves at a corrugated interface between two dissimilar monoclinic elastic half-spaces. – Int. J. Solids Struct., vol.44, No.1, pp.197-228.
• [30] Singh S.S. and Tomar S.K. (2008): Corrigendum to quasi P$-waves at a corrugated interface between two dissimilar monoclinic elastic half-spaces. – Int. J. Solids Struct., vol.45, No.11, pp.3610-3621.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019)